Side note: A summary of something I’ve been using for many hardware hacks in the past while.

A lot of commercial machines use gears for transferring forces. Well, duh. It’s often necessary to change gearing around, though, and it’s nigh-impossible to find commercial solutions with appropriate ratios, tooth profiles, and mounting options. So usually I laser cut my own.

The easiest way to generate a gear that meshes with an unknown is to use Inkscape’s Gear extension. It needs circular pitch, which you find by:

Measuring the gear’s outer diameter, OD

Counting the teeth, N

Getting diametral pitch: (N+ 2) / OD

Calculating circular pitch: Pi / Diametral pitch

For the pressure angle, it’s a little more complicated. You need the base pitch:

Use your digital calipers to measure right down in the gaps of two teeth

Measure three teeth

Subtract the two-teeth measure from the three-teeth one to get a single tooth

Do the same for 5 and 4 teeth

Take an average result of those to get an approximate base pitch measurement

Base Pitch * Diametral Pitch = Pi * Cos(Pressure Angle)

Of course, that looks difficult and error-prone but generally you’ll only run into pressure angles of 14.5 or 20 degrees, so only do rough measurements pick the closest one.

For mounting holes, you’ll need to know how far apart to space them. Pitch diameter is what you need: Teeth / Diametral pitch

This is a quick summary of everything you need to know. There are a lot of dimensions associated with spur gears, and it’s good to know what’s what, but these are the only ones you actually need to make your own. All of these formulas are unitless, so pick and choose, as long as you match the same unit in Inkscape. I uses inches for these, but I tend to switch back and forth to metric with impunity for everything else.